Honors Geometry Sections
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1 Honors Geometry Sections Name Determine whether the figure has rotational symmetry. If so, describe the rotations that map the figure onto itself Use the diagram to complete each sentence o clockwise rotation of AB about point P is o clockwise rotation of KF about point P is o counterclockwise rotation of CE about point P is o rotation of KEF about point P is o rotation of BCJ about point P is o clockwise rotation of APG about point P is. Name the coordinates of the vertices of the image after a clockwise rotation of the given number of degrees about the origin o o o
2 Graph the image of the figure using the following rotation about the origin. 13. rotation of 90 o clockwise 14. rotation of 180 o clockwise Find the angle of rotation that maps ABC onto A"B"C" Fill in the following properties. 17. If (x, y) is reflected over the x-axis, its image is the point (, ). 18. If (x, y) is reflected over the y-axis, its image is the point (, ). 19. If (x, y) is reflected over the y = x, its image is the point (, ). 20. If (x, y) is rotated 90 o clockwise rotation about the origin, its image is the point (, ). 21. If (x, y) is rotated 180 o clockwise rotation about the origin, its image is the point (, ). 22. If (x, y) is rotated 270 o clockwise rotation about the origin, its image is the point (, ). Find the coordinates of the reflection without using a coordinate plane. 23. Point L with coordinates of (2, 3) reflected in the line x = Point M with coordinates of ( 2, 4) reflected in the line y = Point N with coordinates of ( 4, 0) reflected in the line x = Point P with coordinates of (8, 3) reflected in the liney = 4.
3 Match the composition with the diagram, in which figure 1 is the preimage of figure 2, and figure 2 is the preimage of figure Rotate about point P, then reflected in line m. 28. Reflected in line m, then rotated about point P. 29. Translated parallel to line m, then rotated about point P. Describe the composition (translation, reflection, rotation), along with the amount of the transformation from ABC A B C A B C ABC A B C : A B C A B C : ABC A B C : A B C A B C : For #32 and 33, the first translation maps point A to point A and the second translation maps point A to point A. Find the translation that maps point A to point A. 32. Point A: ( 1, 6) 33. Point A: (5, 14) Translation 1: (x, y) (x + 7, y 2) Translation 1: (x, y) (x 8, y 3) Translation 2: (x, y) (x 9, y 5) Translation 2: (x, y) (x 4, y + 6) Point A : Point A :
4 Use the information below to sketch the image of ABC after the composition. 34. Coordinates: A( 6, 6), B( 2, 4), C( 4, 1) Reflection: in the x-axis Rotation: 270 o clockwise Reflection A B C Rotation A B C 35. Coordinates: A(4, 6), B(4, 2), C(1, 2) Rotation: 90 o clockwise Reflection: in the x-axis Rotation A B C Reflection A B C 36. Coordinates: A( 5, 6), B( 3, 4), C( 4, 3) Translation: (x, y) (x + 6, y 2) Rotation: 90 o clockwise Translation A B C Rotation A B C
5 For #37 42, R k : A A. Find an equation of line k A reflection maps point Q( 1, 8) to point Q (2, 0). Find the equation of the line of the reflection. 44. A reflection maps point Q(5, 3) to point Q ( 4, 10). Find the equation of the line of the reflection. Use coordinate notation to describe the translation units to the right and 2 units down units up and 4 units to the right units to the left and 1 unit up units down and 5 units to the left Describe the translation using (a) coordinate notation and (b) a vector in component form
6 For #51 53, determine the new coordinates given the translation. 51. If A: (0, 0) (5, 1), then A: (3, 3) (, ). 52. If A: (1, 1) (3, 0), then A: (0, 0) (, ). 53. If A: ( 2, 3) (2, 6), then A: (, ) (0, 0). The diagonals of regular hexagon ABCDEF form six equilateral triangles as shown. Complete each statement below. 54. R O. 60 : E 55. R O. 60 : D 56. R O. 120 : F 57. R O.60 : O 58. R O. 60 : O 58. R O.180 : A 59. R O. 240 : C 60. R O. 300 : B Give the equation of the line y = x 2 after a rotation about the origin through the given angle. Then describe the relationship (parallel, perpendicular, collinear, or neither) between the equations of the image and preimage Fill in the other boxes by starting with the preimage and performing a translation, then a reflection of the translation, and finally a rotation of 90 o of the reflection.
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